You will then see Internal Speakers (Type built-in) highlighted in the window.

Adjust the output volume (which also controls the chime volume) in the slider at the bottom of the window. Remember if you mute it there will be no internal speaker sound.

To set the volume for your external speakers:

Plug in speakers or headphones to the headphone jack.

Go to System Prefs > Sound >, then click on the Output tab.

You will then see Headphones (Type built-in) highlighted in the window.

Adjust the output volume (which controls the chime volume in the external speakers) with the slider at the bottom of the window. Remember if you mute it there will be no external speaker sound.

These will not completely mute the startup sound. Muting the internal speaker will make it a lot more silent if you use headphones. But the startup chime will still be there in the headphone speakers. If you mute the headphone too, then you'll get rid of the startup chime for good ... but you'll have to unmute/mute every time you want to use the headphones or want to reboot.

There's a utility called StartupSound.prefPane and it works, but only with Snow Leopard (10.6.*) and previous Mac OS X versions. For Lion and onwards this won't work though.

And there's the SystemAudioVolume trick. Note that some had success with sudo nvram SystemAudioVolume=%80﻿, while others with sudo nvram SystemAudioVolume=%00.﻿ On my Mac the default value was %aa and setting %00 worked. However after a reboot the value was set to %e8 (and the startup chime was still silent).